Since 2019, UK personal taxes (income tax and national insurance) have been increasing as a proportion of incomes and total tax revenues have been increasing as a proportion of GDP. However, in his Autumn Statement of 22 November, the Chancellor, Jeremy Hunt, announced a 2 percentage point cut in the national insurance rate for employees from 12% to 10%. The government hailed this as a significant tax cut. But, despite this, taxes are set to continue increasing. According to the Office for Budget Responsibility (OBR), from 2019/20 to 2028/29, taxes will have increased by 4.5 per cent of GDP (see chart below), raising an extra £44.6 billion per year by 2028/29. One third of this is the result of ‘fiscal drag’ from the freezing of tax thresholds.
According to the OBR
Fiscal drag is the process by which faster growth in earnings than in income tax thresholds results in more people being subject to income tax and more of their income being subject to higher tax rates, both of which raise the average tax rate on total incomes.
Income tax thresholds have been unchanged for the past three years and the current plan is that they will remain frozen until at least 2027/28. This is illustrated in the following table.
If there were no inflation, fiscal drag would still apply if real incomes rose. In other words, people would be paying a higher average rate of tax. Part of the reason is that some people on low incomes would be dragged into paying tax for the first time and more people would be paying taxes at higher rates. Even in the case of people whose income rise did not pull them into a higher tax bracket (i.e. they were paying the same marginal rate of tax), they would still be paying a higher average rate of tax as the personal allowance would account for a smaller proportion of their income.
Inflation compounds this effect. Tax bands are in nominal not real terms. Assume that real incomes stay the same and that tax bands are frozen. Nominal incomes will rise by the rate of inflation and thus fiscal drag will occur: the real value of the personal allowance will fall and a higher proportion of incomes will be paid at higher rates. Since 2021, some 2.2 million workers, who previously paid no income taxes as their incomes were below the personal allowance, are now paying tax on some of their wages at the 20% rate. A further 1.6 million workers have moved to the higher tax bracket with a marginal rate of 40%.
The net effect is that, although national insurance rates have been cut by 2 percentage points, the tax burden will continue rising. The OBR estimates that by 2027/28, tax revenues will be 37.4% of GDP; they were 33.1% in 2019/20. This is illustrated in the chart (click here for a PowerPoint).
Much of this rise will be the result of fiscal drag. According to the OBR, fiscal drag from freezing personal allowances, even after the cut in national insurance rates, will raise an extra £42.9 billion per year by 2027/28. This would be equivalent of the amount raised by a rise in national insurance rates of 10 percentage points. By comparison, the total cost to the government of the furlough scheme during the pandemic was £70 billion. For further analysis by the OBR of the magnitude of fiscal drag, see Box 3.1 (p 69) in the November 2023 edition of its Economic and fiscal outlook.
Support measures during the pandemic and its aftermath and subsidies for energy bills have led to a rise in government debt. This has put a burden on public finances, compounded by sluggish growth and higher interest rates increasing the cost of servicing government debt. This leaves the government (and future governments) in a dilemma. It must either allow fiscal drag to take place by not raising allowances or even raise tax rates, cut government expenditure or increase borrowing; or it must try to stimulate economic growth to provide a larger tax base; or it must do some combination of all of these. These are not easy choices. Higher economic growth would be the best solution for the government, but it is difficult for governments to achieve. Spending on infrastructure, which would support growth, is planned to be cut in an attempt to reduce borrowing. According to the OBR, under current government plans, public-sector net investment is set to decline from 2.6% of GDP in 2023/24 to 1.8% by 2028/29.
The government is attempting to achieve growth by market-orientated supply-side measures, such as making permanent the current 100% corporation tax allowance for investment. Other measures include streamlining the planning system for commercial projects, a business rates support package for small businesses and targeted government support for specific sectors, such as digital technology. Critics argue that this will not be sufficient to offset the decline in public investment and renew crumbling infrastructure.
To support public finances, the government is using a combination of higher taxation, largely through fiscal drag, and cuts in government expenditure (from 44.8% of GDP in 2023/24 to a planned 42.7% by 2028/29). If the government succeeds in doing this, the OBR forecasts that public-sector net borrowing will fall from 4.5% of GDP in 2023/24 to 1.1% by 2028/29. But higher taxes and squeezed public expenditure will make many people feel worse off, especially those that rely on public services.
- Fiscal drag
Sky News Politics Hub on X, Sophy Ridge (22/11/23)
- Fiscal drag
Sky News Politics Hub on X, Beth Rigby (22/11/23)
- Autumn Statement 2023 response
IFS, Stuart Adam, Bee Boileau, Isaac Delestre, Carl Emmerson, Paul Johnson, Robert Joyce, Martin Mikloš, Helen Miller, David Phillips, Sam Ray-Chaudhuri, Isabel Stockton Tom Waters, Tom Wernham and Ben Zaranko (22/11/23)
- Autumn Statement: Jeremy Hunt cuts National Insurance but tax burden still rises
BBC News, Brian Wheeler (23/11/23)
- The hidden tax rise in the Autumn Statement
BBC News, Michael Race (23/11/23)
- How is National Insurance changing and what is income tax?
BBC News (23/11/23)
- UK income tax: how fiscal drag leads to people falling into higher rates
The Guardian, Antonio Voce and Ashley Kirk (22/11/23)
- Will I be pulled into a higher tax band? How ‘fiscal drag’ affects your pay
i News, Alex Dakers (23/11/23)
- Fiscal drag could cost high earners £4,000 by 2027
MoneyWeek, Marc Shoffman (16/11/23)
- Why the UK government’s tax cuts still leave workers worse off
CNBC, Elliot Smith (23/11/23)
- National insurance cuts swamped by stealth tax rise, says fiscal watchdog
Financial Times, Emma Agyemang (22/11/23)
- Frozen income tax bands eat into benefits of NI cut, say experts
FT Adviser, Tara O’Connor (23/11/23)
- Jeremy Hunt’s fiscal fudge
Financial Times editorial (22/11/23)
Report and data from the OBR
- Would fiscal drag occur with frozen nominal tax bands if there were zero real growth in incomes? Explain.
- Examine the arguments for continuing to borrow to fund a Budget deficit over a number of years.
- When interest rates rise, how much does this affect the cost of servicing public-sector debt? Why is the effect likely to be greater in the long run than in the short run?
- If the government decides that it wishes to increase tax revenues as a proportion of GDP (for example, to fund increased government expenditure on infrastructure and socially desirable projects and benefits), examine the arguments for increasing personal allowances and tax bands in line with inflation but raising the rates of income tax in order to raise sufficient revenue?
- Distinguish between market-orientated and interventionist supply-side policies? Why do political parties differ in their approaches to supply-side policy?
The past decade or so has seen large-scale economic turbulence. As we saw in the blog Fiscal impulses, governments have responded with large fiscal interventions. The COVID-19 pandemic, for example, led to a positive fiscal impulse in the UK in 2020, as measured by the change in the structural primary balance, of over 12 per cent of national income.
The scale of these interventions has led to a significant increase in the public-sector debt-to-GDP ratio in many countries. The recent interest rates hikes arising from central banks responding to inflationary pressures have put additional pressure on the financial well-being of governments, not least on the financing of their debt. Here we discuss these pressures in the context of the ‘r – g’ rule of sustainable public debt.
Public-sector debt and borrowing
Chart 1 shows the path of UK public-sector net debt and net borrowing, as percentages of GDP, since 1990. Debt is a stock concept and is the result of accumulated flows of past borrowing. Net debt is simply gross debt less liquid financial assets, which mainly consist of foreign exchange reserves and cash deposits. Net borrowing is the headline measure of the sector’s deficit and is based on when expenditures and receipts (largely taxation) are recorded rather than when cash is actually paid or received. (Click here for a PowerPoint of Chart 1)
Chart 1 shows the impact of the fiscal interventions associated with the global financial crisis and the COVID-19 pandemic, when net borrowing rose to 10 per cent and 15 per cent of GDP respectively. The former contributed to the debt-to-GDP ratio rising from 35.6 per cent in 2007/8 to 81.6 per cent in 2014/15, while the pandemic and subsequent cost-of-living interventions contributed to the ratio rising from 85.2 per cent in 2019/20 to around 98 per cent in 2023/24.
Sustainability of the public finances
The ratcheting up of debt levels affects debt servicing costs and hence the budgetary position of government. Yet the recent increases in interest rates also raise the costs faced by governments in financing future deficits or refinancing existing debts that are due to mature. In addition, a continuation of the low economic growth that has beset the UK economy since the global financial crisis also has implications for the burden imposed on the public sector by its debts, and hence the sustainability of the public finances. After all, low growth has implications for spending commitments, and, of course, the flow of receipts.
The analysis therefore implies that the sustainability of public-sector debt is dependent on at least three factors: existing debt levels, the implied average interest rate facing the public sector on its debts, and the rate of economic growth. These three factors turn out to underpin a well-known rule relating to the fiscal arithmetic of public-sector debt. The rule is sometimes known as the ‘r – g’ rule (i.e. the interest rate minus the growth rate).
Underpinning the fiscal arithmetic that determines the path of public-sector debt is the concept of the ‘primary balance’. This is the difference between the sector’s receipts and its expenditures less its debt interest payments. A primary surplus (a positive primary balance) means that receipts exceed expenditures less debt interest payments, whereas a primary deficit (a negative primary balance) means that receipts fall short. The fiscal arithmetic necessary to prevent the debt-to-GDP ratio rising produces the following stable debt equation or ‘r – g’ rule:
On the left-hand side of the stable debt equation is the required primary surplus (PS) to GDP (Y) ratio. Moving to the right-hand side, the first term is the existing debt-to-GDP ratio (D/Y). The second term ‘r – g’, is the differential between the average implied interest rate the government pays on its debt and the growth rate of the economy. These terms can be expressed in either nominal or real terms as this does not affect the differential.
To illustrate the rule consider a country whose existing debt-to-GDP ratio is 1 (i.e. 100 per cent) and the ‘r – g’ differential is 0.02 (2 percentage points). In this scenario they would need to run a primary surplus to GDP ratio of 0.02 (i.e. 2 percent of GDP).
The ‘r – g‘ differential
The ‘r – g’ differential reflects macroeconomic and financial conditions. The fiscal arithmetic shows that these are important for the dynamics of public-sector debt. The fiscal arithmetic is straightforward when r = g as any primary deficit will cause the debt-to-GDP ratio to rise, while a primary surplus will cause the ratio to fall. The larger is g relative to r the more favourable are the conditions for the path of debt. Importantly, if the differential is negative (r < g), it is possible for the public sector to run a primary deficit, up to the amount that the stable debt equation permits.
Consider Charts 2 and 3 to understand how the ‘r – g’ differential has affected debt sustainability in the UK since 1990. Chart 2 plots the implied yield on 10-year government bonds, alongside the annual rate of nominal growth (click here for a PowerPoint). As John explains in his blog The bond roller coaster, the yield is calculated as the coupon rate that would have to be paid for the market price of a bond to equal its face value. Over the period, the average annual nominal growth rate was 4.5 per cent, while the implied interest rate was almost identical at 4.6 per cent. The average annual rate of CPI inflation over this period was 2.8 per cent.
Chart 3 plots the ‘r – g’ differential which is simply the difference between the two series in Chart 2, along with a 12-month rolling average of the differential to help show better the direction of the differential by smoothing out some of the short-term volatility (click here for a PowerPoint). The differential across the period is a mere 0.1 percentage points implying that macroeconomic and financial conditions have typically been neutral in supporting debt sustainability. However, this does mask some significant changes across the period.
We observe a general downward trend in the ‘r – g’ differential from 1990 up to the time of the global financial crisis. Indeed between 2003 and 2007 we observe a favourable negative differential which helps to support the sustainability of public debt and therefore the well-being of the public finances. This downward trend of the ‘r – g’ differential was interrupted by the financial crisis, driven by a significant contraction in economic activity. This led to a positive spike in the differential of over 7 percentage points.
Yet the negative differential resumed in 2010 and continued up to the pandemic. Again, this is indicative of the macroeconomic and financial environments being supportive of the public finances. It was, however, largely driven by low interest rates rather than by economic growth.
Consequently, the negative ‘r – g’ differential meant that the public sector could continue to run primary deficits during the 2010s, despite the now much higher debt-to-GDP ratio. Yet, weak growth was placing limits on this. Chart 4 indeed shows that primary deficits fell across the decade (click here for a PowerPoint).
The pandemic and beyond
The pandemic saw the ‘r – g’ differential again turn markedly positive, averaging 7 percentage points in the four quarters from Q2 of 2020. While the differential again turned negative, the debt-to-GDP ratio had also increased substantially because of large-scale fiscal interventions. This made the negative differential even more important for the sustainability of the public finances. The question is how long the negative differential can last.
Looking forward, the fiscal arithmetic is indeed uncertain and worryingly is likely to be less favourable. Interest rates have risen and, although inflationary pressures may be easing somewhat, interest rates are likely to remain much higher than during the past decade. Geopolitical tensions and global fragmentation pose future inflationary concerns and a further drag on growth.
As well as the short-term concerns over growth, there remain long-standing issues of low productivity which must be tackled if the growth of the UK economy’s potential output is to be raised. These concerns all point to the important ‘r – g’ differential become increasingly less negative, if not positive. If so the fiscal arithmetic could mean increasingly hard maths for policymakers.
- The budget deficit: a short guide
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- If markets are right about long real rates, public debt ratios will increase for some time. We must make sure that they do not explode.
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- The UK government’s debt nightmare
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- National debt could hit 300% of GDP by 2070s, independent watchdog the OBR warns
Sky News, James Sillars (13/7/23)
- How much money is the UK government borrowing, and does it matter?
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- Cost of national debt hits 20-year high
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- Bond markets could see ‘mini boom-bust cycles’ as global government debt to soar by $5 trillion a yea
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- The counterintuitive truth about deficits for bond investors
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- UK government borrowing almost £20bn lower than expected
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- Controlling debt is just a means — it is not a government’s end
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- What is meant by each of the following terms: (a) net borrowing; (b) primary deficit; (c) net debt?
- Explain how the following affect the path of the public-sector debt-to-GDP ratio: (a) interest rates; (b) economic growth; (c) the existing debt-to-GDP ratio.
- Which factors during the 2010s were affecting the fiscal arithmetic of public debt positively, and which negatively?
- Discuss the prospects for the fiscal arithmetic of public debt in the coming years.
- Assume that a country has an existing public-sector debt-to-GDP ratio of 60 percent.
(a) Using the ‘rule of thumb’ for public debt dynamics, calculate the approximate primary balance it would need to run in the coming year if the expected average real interest rate on the debt were 3 per cent and real economic growth were 2 per cent?
(b) Repeat (a) but now assume that real economic growth is expected to be 4 per cent.
(c) Repeat (a) but now assume that the existing public-sector debt-to-GDP ratio is 120 per cent.
(d) Using your results from (a) to (c) discuss the factors that affect the fiscal arithmetic of the growth of public-sector debt.
In his blog, The bond roller coaster, John looks at the pricing of government bonds and details how, in recent times, governments wishing to borrow by issuing new bonds are having to offer higher coupon rates to attract investors. The interest rate hikes by central banks in response to global-wide inflationary pressures have therefore spilt over into bond markets. Though this evidences the ‘pass through’ of central bank interest rate increases to the general structure of interest rates, it does, however, pose significant costs for governments as they seek to finance future budgetary deficits or refinance existing debts coming up to maturity.
The Autumn Statement in the UK is scheduled to be made on 22 November. This, as well as providing an update on the economy and the public finances, is likely to include a number of fiscal proposals. It is thus timely to remind ourselves of the size of recent discretionary fiscal measures and their potential impact on the sustainability of the public finances. In this first of two blogs, we consider the former: the magnitude of recent discretionary fiscal policy changes.
First, it is important to define what we mean by discretionary fiscal policy. It refers to deliberate changes in government spending or taxation. This needs to be distinguished from the concept of automatic stabilisers, which relate to those parts of government budgets that automatically result in an increase (decrease) of spending or a decrease (increase) in tax payments when the economy slows (quickens).
The suitability of discretionary fiscal policy measures depends on the objectives they trying to fulfil. Discretionary measures can be implemented, for example, to affect levels of public-service provision, the distribution of income, levels of aggregate demand or to affect longer-term growth of aggregate supply. As we shall see in this blog, some of the large recent interventions have been conducted primarily to support and stabilise economic activity in the face of heightened economic volatility.
Discretionary fiscal measures in the UK are usually announced in annual Budget statements in the House of Commons. These are normally in March, but discretionary fiscal changes can be made in the Autumn Statement too. The Autumn Statement of October 2022, for example, took on significant importance as the new Chancellor of the Exchequer, Jeremy Hunt, tried to present a ‘safe pair hands’ following the fallout and market turbulence in response to the fiscal statement by the former Chancellor, Kwasi Kwarteng, on 23 September that year.
The fiscal impulse
The large-scale economic turbulence of recent years associated first with the global financial crisis of 2007–9 and then with the COVID-19 pandemic and the cost-of-living crisis, has seen governments respond with significant discretionary fiscal measures. During the COVID-19 pandemic, examples of fiscal interventions in the UK included the COVID-19 Business Interruption Loan Scheme (CBILS), grants for retail, hospitality and leisure businesses, the COVID-19 Job Retention Scheme (better known as the furlough scheme) and the Self-Employed Income Support Scheme.
The size of discretionary fiscal interventions can be measured by the fiscal impulse. This captures the magnitude of change in discretionary fiscal policy and thus the size of the stimulus. The concept is not to be confused with fiscal multipliers, which measure the impact of fiscal changes on economic outcomes, such as real national income and employment.
By measuring fiscal impulses, we can analyse the extent to which a country’s fiscal stance has tightened, loosened, or remained unchanged. In other words, we are attempting to capture discretionary fiscal policy changes that result in structural changes in the government budget and, therefore, in structural changes in spending and/or taxation.
To measure structural changes in the public-sector’s budgetary position, we calculate changes in structural budget balances.
A budget balance is simply the difference between receipts (largely taxation) and spending. A budget surplus occurs when receipts are greater than spending, while a deficit (sometimes referred to as net borrowing) occurs if spending is greater than receipts.
A structural budget balance cyclically-adjusts receipts and spending and hence adjusts for the position of the economy in the business cycle. In doing so, it has the effect of adjusting both receipts and spending for the effect of automatic stabilisers. Another way of thinking about this is to ask what the balance between receipts and spending would be if the economy were operating at its potential output. A deterioration in a structural budget balance infers a rise in the structural deficit or fall in the structural surplus. This indicates a loosening of the fiscal stance. An improvement in the structural budget balance, by contrast, indicates a tightening.
The size of UK fiscal impulses
A frequently-used measure of the fiscal impulse involves the change in the cyclically-adjusted public-sector primary deficit.
A primary deficit captures the extent to which the receipts of the public sector fall short of its spending, excluding its spending on debt interest payments. It essentially captures whether the public sector is able to afford its ‘new’ fiscal choices from its receipts; it excludes debt-servicing costs, which can be thought of as reflecting fiscal choices of the past. By using a cyclically-adjusted primary deficit we are able to isolate more accurately the size of discretionary policy changes. Chart 1 shows the UK’s actual and cyclically-adjusted primary deficit as a share of GDP since 1975, which have averaged 1.3 and 1.1 per cent of GDP respectively. (Click here for a PowerPoint of the chart.)
The size of the fiscal impulse is measured by the year-on-year percentage point change in the cyclically-adjusted public-sector primary deficit as a percentage of potential GDP. A larger deficit or a smaller surplus indicates a fiscal loosening (a positive fiscal impulse), while a smaller deficit or a larger surplus indicates a fiscal tightening (a negative fiscal impulse).
Chart 2 shows the magnitude of UK fiscal impulses since 1980. It captures very starkly the extent of the loosening of the fiscal stance in 2020 in response to the COVID-19 pandemic. (Click here for a PowerPoint of the chart.) In 2020 the cyclically-adjusted primary deficit to potential output ratio rose from 1.67 to 14.04 per cent. This represents a positive fiscal impulse of 12.4 per cent of GDP.
A tightening of fiscal policy followed the waning of the pandemic. 2021 saw a negative fiscal impulse of 10.1 per cent of GDP. Subsequent tightening was tempered by policy measures to limit the impact on the private sector of the cost-of-living crisis, including the Energy Price Guarantee and Energy Bills Support Scheme.
In comparison, the fiscal response to the global financial crisis led to a cumulative increase in the cyclically-adjusted primary deficit to potential GDP ratio from 2007 to 2009 of 5.0 percentage points. Hence, the financial crisis saw a positive fiscal impulse of 5 per cent of GDP. While smaller in comparison to the discretionary fiscal responses to the COVID-19 pandemic, it was, nonetheless, a sizeable loosening of the fiscal stance.
Sustainability and well-being of the public finances
The recent fiscal interventions have implications for the financial well-being of the public-sector. Not least, the financing of the positive fiscal impulses has led to a substantial growth in the accumulated size of the public-sector debt stock. At the end of 2006/7 the public-sector net debt stock was 35 per cent of GDP; at the end of the current financial year, 2023/24, it is expected to be 103 per cent.
As we saw at the outset, in an environment of rising interest rates, the increase in the public-sector debt to GDP ratio creates significant additional costs for government, a situation that is made more difficult for government not only by the current flatlining of economic activity, but by the low underlying rate of economic growth seen since the financial crisis. The combination of higher interest rates and lower economic growth has adverse implications for the sustainability of the public finances and the ability of the public sector to absorb the effects of future economic crises.
- Autumn Statement 2023: When is it and how will it affect me?
BBC News (16/11/23)
- What is the Autumn Statement?
House of Commons Library (13/11/23)
- Putting the fiscal toothpaste back into the tube: It’s time to normalise the euro area fiscal stance in 2024
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- Euro zone should tighten fiscal policy in 2024 to curb inflation, European Fiscal Board says
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- Hutchins Center Fiscal Impact Measure: Federal, State and Local Fiscal Policy and the Economy
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- IFS Green Budget
Institute for Fiscal Studies, Carl Emmerson, Paul Johnson and Ben Zaranko (eds) (October 2023)
- Explain what is meant by the following fiscal terms: (a) structural deficit; (b) automatic stabilisers; (c) discretionary fiscal policy; (d) primary deficit.
- What is the difference between current and capital public expenditures? Give some examples of each.
- Consider the following two examples of public expenditure: grants from government paid to the private sector for the installation of energy-efficient boilers, and welfare payments to unemployed people. How are these expenditures classified in the public finances and what fiscal objectives do you think they meet?
- Which of the following statements about the primary balance is FALSE?
(a) In the presence of debt interest payments a primary deficit will be smaller than a budget deficit.
(b) In the presence of debt interest payments a primary surplus will be smaller than a budget surplus.
(c) The primary balance differs from the budget balance by the size of debt interest payments.
(d) None of the above.
- Explain the difference between a fiscal impulse and a fiscal multiplier.
- Why is low economic growth likely to affect the sustainability of the public finances? What other factors could also matter?
To finance budget deficits, governments have to borrow. They can borrow short-term by issuing Treasury bills, typically for 1, 3 or 6 months. These do not earn interest and hence are sold at a discount below the face value. The rate of discount depends on supply and demand and will reflect short-term market rates of interest. Alternatively, governments can borrow long-term by issuing bonds. In the UK, these government securities are known as ‘gilts’ or ‘gilt-edged securities’. In the USA they are known as ‘treasury bonds’, ‘T-bonds’ or simply ‘treasuries’. In the EU, countries separately issue bonds but the European Commission also issues bonds.
In the UK, gilts are issued by the Debt Management Office on behalf of the Treasury. Although there are index-linked gilts, the largest proportion of gilts are conventional gilts. These pay a fixed sum of money per annum per £100 of face value. This is known as the ‘coupon payment’ and the rate is set at the time of issue. The ‘coupon rate’ is the payment per annum as a percentage of the bond’s face value:
Payments are made six-monthly. Each issue also has a maturity date, at which point the bonds will be redeemed at face value. For example, a 4½% Treasury Gilt 2028 bond has a coupon rate of 4½% and thus pays £4.50 per annum (£2.25 every six months) for each £100 of face value. The issue will be redeemed in June 2028 at face value. The issue was made in June 2023 and thus represented a 5-year bond. Gilts are issued for varying lengths of time from 2 to 55 years. At present, there are 61 different conventional issues of bonds, with maturity dates varying from January 2024 to October 2073.
Bonds can be sold on the secondary market (i.e. the stock market) before maturity. The market price, however, is unlikely to be the coupon price (i.e. the face value). The lower the coupon rate relative to current interest rates, the less valuable the bond will be. For example, if interest rates rise, and hence new bonds pay a higher coupon rate, the market price of existing bonds paying a lower coupon rate must fall. Thus bond prices vary inversely with interest rates.
The market price also depends on how close the bonds are to maturity. The closer the maturity date, the closer the market price of the bond will be to the face value.
Bond yields: current yield
A bond’s yield is the percentage return that a person buying the bond receives. If a newly issued bond is bought at the coupon price, its yield is the coupon rate.
However, if an existing bond is bought on the secondary market (the stock market), the yield must reflect the coupon payments relative to the purchase price, not the coupon price. We can distinguish between the ‘current yield’ and the ‘yield to maturity’.
The current yield is the coupon payment as a percentage of the current market price of the bond:
Assume a bond were originally issued at 2% (its coupon rate) and thus pays £2 per annum. In the meantime, however, assume that interest rates have risen and new bonds now have a coupon rate of 4%, paying £4 per annum for each £100 invested. To persuade people to buy old bonds with a coupon rate of 2%, their market prices must fall below their face value (their coupon price). If their price halved, then they would pay £2 for every £50 of their market price and hence their current yield would be 4% (£2/£50 × 100).
Bond yields: yield to maturity (YTM)
But the current yield does not give the true yield – it is only an approximation. The true yield must take into account not just the market price but also the maturity value and the length of time to maturity (and the frequency of payments too, which we will ignore here). The closer a bond is to its maturity date, the higher/lower will be the true yield if the price is below/above the coupon price: in other words, the closer will the market price be to the coupon price for any given market rate of interest.
A more accurate measure of a bond’s yield is thus the ‘yield to maturity’ (YTM). This is the interest rate which makes the present value of all a bond’s future cash flows equal to its current price. These cash flows include all coupon payments and the payment of the face value on maturity. But future cash flows must be discounted to take into account the fact that money received in the future is worth less than money received now, since money received now could then earn interest.
The yield to maturity is the internal rate of return (IRR) of the bond. This is the discount rate which makes the present value (PV) of all the bond’s future cash flows (including the maturity payment of the coupon price) equal to its current market price. For simplicity, we assume that coupon payments are made annually. The formula is the one where the bond’s current market price is given by:
Where: t is the year; n is the number of years to maturity; YTM is the yield to maturity.
Thus if a bond paid £5 each year and had a maturity value of £100 and if current interest rates were higher than 5%, giving a yield to maturity of 8%, then the bond price would be:
In other words, with a coupon rate of 5% and a higher YTM of 8%, the bond with a face value of £100 and five years to maturity would be worth only £88.02 today.
If you know the market price of a given bond, you can work out its YTM by substituting in the above formula. The following table gives examples.
The higher the YTM, the lower the market price of a bond. Since the YTM reflects in part current rates of interest, so the higher the rate of interest, the lower the market price of any given bond. Thus bond yields vary directly with interest rates and bond prices vary inversely. You can see this clearly from the table. You can also see that market bond prices converge on the face value as the maturity date approaches.
Recent activity in bond markets
Investing in government bonds is regarded as very safe. Coupon payments are guaranteed, as is repayment of the face value on the maturity date. For this reason, many pension funds hold a lot of government bonds issued by financially trustworthy governments. But in recent months, bond prices in the secondary market have fallen substantially as interest rates have risen. For those holding existing bonds, this means that their value has fallen. For governments wishing to borrow by issuing new bonds, the cost has risen as they have to offer a higher coupon rate to attract buyers. This make it more expensive to finance government debt.
The chart shows the yield on 10-year government bonds. It is calculated using the ‘par value’ approach. This gives the coupon rate that would have to be paid for the market price of a bond to equal its face value. Clearly, as interest rates rise, a bond would have to pay a higher coupon rate for this to happen. (This, of course, is only hypothetical to give an estimate of market rates, as coupon rates are fixed at the time of a bond’s issue.)
Par values reflect both yield to maturity and also expectations of future interest rates. The higher people expect future interest rates to be, the higher must par values be to reflect this.
In the years following the financial crisis of 2007–8 and the subsequent recession, and again during the COVID pandemic, central banks cut interest rates and supported this by quantitative easing. This involved central banks buying existing bonds on the secondary market and paying for them with newly created (electronic) money. This drove up bond prices and drove down yields (as the chart shows). This helped support the policy of low interest rates. This was a boon to governments, which were able to borrow cheaply.
This has all changed. With quantitative tightening replacing quantitative easing, central banks have been engaging in asset sales, thereby driving down bond prices and driving up yields. Again, this can be seen in the chart. This has helped to support a policy of higher interest rates.
Problems of higher bond yields/lower bond prices
Although lower bond prices and higher yields have supported a tighter monetary policy, which has been used to fight inflation, this has created problems.
First, it has increased the cost of financing government debt. In 2007/8, UK public-sector net debt was £567bn (35.6% of GDP). The Office for Budget Responsibility forecasts that it will be £2702bn (103.1% of GDP in the current financial year – 2023/24). Not only, therefore, are coupon rates higher for new government borrowing, but the level of borrowing is now a much higher proportion of GDP. In 2020/21, central government debt interest payments were 1.2% of GDP; by 2022/23, they were 4.4% (excluding interest on gilts held in the Bank of England, under the Asset Purchase Facility (quantitative easing)).
In the USA, there have been similar increases in government debt and debt interest payments. Debt has increased from $9tn in 2007 to $33.6tn today. Again, with higher interest rates, debt interest as a percentage of GDP has risen: from 1.5% of GDP in 2021 to a forecast 2.5% in 2023 and 3% in 2024. What is more, 31 per cent of US government bonds will mature next year and will need refinancing – at higher coupon rates.
There is a similar picture in other developed countries. Clearly, higher interest payments leave less government revenue for other purposes, such as health and education.
Second, many pension funds, banks and other investment companies hold large quantities of bonds. As their price falls, so this reduces the value of these companies’ assets and makes it harder to finance new purchases, or payments or loans to customers. However, the fact that new bonds pay higher interest rates means that when existing bond holdings mature, the money can be reinvested at higher rates.
Third, bonds are often used by companies as collateral against which to borrow and invest in new capital. As bond prices fall, this can hamper companies’ ability to invest, which will lead to lower economic growth.
Fourth, higher bond yields divert demand away from equities (shares). With equity markets falling back or at best ceasing to rise, this erodes the value of savings in equities and may make it harder for firms to finance investment through new issues.
At the core of all these problems is inflation and budget deficits. Central banks have responded by raising interest rates. This drives up bond yields and drives down bond prices. But bond prices and yields depend not just on current interest rates, but also on expectations about future interest rates. Expectations currently are that budget deficits will be slow to fall as governments seek to support their economies post-COVID. Also expectations are that inflation, even though it is falling, is not falling as fast as originally expected – a problem that could be exacerbated if global tensions increase as a result of the ongoing war in Ukraine, the Israel/Gaza war and possible increased tensions with China concerning disputes in the China Sea and over Taiwan. Greater risks drive up bond yields as investors demand a higher interest premium.
Information and data
- Why do bond prices and bond yields vary inversely?
- How are bond yields and prices affected by expectations?
- Why are ‘current yield’ and ‘yield to maturity’ different?
- What is likely to happen to bond prices and yields in the coming months? Explain your reasoning.
- What constraints do bond markets place on fiscal policy?
- Would it be desirable for central banks to pause their policy of quantitative tightening?
We have examined inflation in several blogs in recent months. With inflation at levels not seen for 40 years, this is hardly surprising. One question we’ve examined is whether the policy response has been correct. For example, in July, we asked whether the Bank of England had raised interest rates too much, too late. In judging policy, one useful distinction is between demand-pull inflation and cost-push inflation. Do they require the same policy response? Is raising interest rates to get inflation down to the target rate equally applicable to inflation caused by excessive demand and inflation caused by rising costs, where those rising costs are not caused by rising demand?
In terms of aggregate demand and supply, demand-pull inflation is shown by continuing rightward shifts in aggregate demand (AD); cost-push inflation is shown by continuing leftward/upward shifts in short-run aggregate supply (SRAS). This is illustrated in the following diagram, which shows a single shift in aggregate demand or short-run aggregate supply. For inflation to continue, rather than being a single rise in prices, the curves must continue to shift.
As you can see, the effects on real GDP (Y) are quite different. A rise in aggregate demand will tend to increase GDP (as long as capacity constraints allow). A rise in costs, and hence an upward shift in short-run aggregate supply, will lead to a fall in GDP as firms cut output in the face of rising costs and as consumers consume less as the cost of living rises.
The inflation experienced by the UK and other countries in recent months has been largely of the cost-push variety. Causes include: supply-chain bottlenecks as economies opened up after COVID-19; the war in Ukraine and its effects on oil and gas supplies and various grains; and avian flu and poor harvests from droughts and floods associated with global warming resulting in a fall in food supplies. These all led to a rise in prices. In the UK’s case, this was compounded by Brexit, which added to firms’ administrative costs and, according to the Bank of England, was estimated to cause a long-term fall in productivity of around 3 to 4 per cent.
The rise in costs had the effect of shifting short-run aggregate supply upwards to the left. As well as leading to a rise in prices and a cost-of-living squeeze, the rising costs dampened expenditure.
This was compounded by a tightening of fiscal policy as governments attempted to tackle public-sector deficits and debt, which had soared with the support measures during the pandemic. It was also compounded by rising interest rates as central banks attempted to bring inflation back to target.
Monetary policy response
Central banks are generally charged with keeping inflation in the medium term at a target rate set by the government or the central bank itself. For most developed countries, this is 2% (see table in the blog, Should central bank targets be changed?). So is raising interest rates the correct policy response to cost-push inflation?
One argument is that monetary policy is inappropriate in the face of supply shocks. The supply shocks themselves have the effect of dampening demand. Raising interest rates will compound this effect, resulting in lower growth or even a recession. If the supply shocks are temporary, such as supply-chain disruptions caused by lockdowns during the pandemic, then it might be better to ride out the problem and not raise interest rates or raise them by only a small amount. Already cost pressures are easing in some areas as supplies have risen.
If, however, the fall in aggregate supply is more persistent, such as from climate-related declines in harvests or the Ukraine war dragging on, or new disruptions to supply associated with the Israel–Gaza war, or, in the UK’s case, with Brexit, then real aggregate demand may need to be reduced in order to match the lower aggregate supply. Or, at the very least, the growth in aggregate demand may need to be slowed to match the slower growth in aggregate supply.
Huw Pill, the Chief Economist at the Bank of England, in a podcast from the Columbia Law School (see links below), argued that people should recognise that the rise in costs has made them poorer. If they respond to the rising costs by seeking higher wages, or in the case of businesses, by putting up prices, this will simply stoke inflation. In these circumstances, raising interest rates to cool aggregate demand may reduce people’s ability to gain higher wages or put up prices.
Another argument for raising interest rates in the face of cost-push inflation is when those cost increases are felt more than in other countries. The USA has suffered less from cost pressures than the UK. On the other hand, its growth rate is higher, suggesting that its inflation, albeit lower than in the UK, is more of the demand-pull variety. Despite its inflation rate being lower than in the UK, the problem of excess demand has led the Fed to adopt an aggressive interest rate policy. Its target rate is 5.25% to 5.50%, while the Bank of England’s is 5.25%. In order to prevent short-term capital outflows and a resulting depreciation in the pound, further stoking inflation, the Bank of England has been under pressure to mirror interest rate rises in the USA, the eurozone and elsewhere.
Blogs on this site
Information and data
- How may monetary policy affect inflationary expectations?
- If cost-push inflation makes people generally poorer, what role does the government have in making the distribution of a cut in real income a fair one?
- In the context of cost-push inflation, how might the authorities prevent a wage–price spiral?
- With reference to the second article above, explain the ‘monetary policy conundrum’ faced by the Bank of Japan.
- If central banks have a single policy instrument, namely changes in interest rates, how may conflicts arise when there is more than one macroeconomic objective?
- Is Russia’s rise in inflation the result of cost or demand pressures, or a mixture of the two (see articles above)?